Elongated Bose-Einstein Condensate Research Articles

Stability analysis and attractor dynamics of three-dimensional dark solitons with localized dissipation

We study the stability and the attractor dynamics of an elongated Bose-Einstein condensate with dark or grey kink solitons in the presence of localized dissipation. To this end, the 3D Gross-Pitaevskii equation with an additional imaginary potential is solved numerically. We analyze the suppression of the snaking instability in dependence of the dissipation strength and extract the threshold value for the stabilization of the dark soliton for experimentally realistic parameters. Below the threshold value, we observe the decay into a solitonic vortex. Above the stabilization threshold, we observe the attractor dynamics towards the dark soliton when initially starting from a grey soliton. We find that for all initial conditions the dark soliton is the unique steady-state of the system - even when starting from the BEC ground state.

Dispersion relations and self-localization of quasiparticles in coupled elongated Bose-Einstein condensates

We present a detailed study of the spectrum and dispersion of Bogoliubov quasiparticles in two coupled elongated Bose-Einstein condensates. We develop an analytically solvable model that approximates two infinite homogeneous condensates and compare its predictions to a numerical simulation of a realistic trapped system. While the comparisons show a reasonable agreement between the two models, they also manifest the existence of several anomalous Bogoliubov modes in the spectrum. These modes show degeneracy in both energy and momentum together with self-localization in the coordinate space.

Breathing mode of a Bose-Einstein condensate repulsively interacting with a fermionic reservoir

We investigate the fundamental breathing mode of a small-sized elongated Bose-Einstein condensate coupled to a large Fermi sea of atoms. Our observations show a dramatic shift of the breathing frequency when the mixture undergoes phase separation at strong interspecies repulsion. We find that the maximum frequency shift in the full phase-separation limit depends essentially on the atom number ratio of the components. We interpret the experimental observations within a model that assumes an adiabatic response of the Fermi sea, or within another model that considers single fermion trajectories for a fully phase-separated mixture. These two complementary models capture the observed features over the full range of interest.

Parametric Excitation of a Bose-Einstein Condensate: From Faraday Waves to Granulation

We explore, both experimentally and theoretically, the response of an elongated Bose-Einstein condensate to modulated interactions. We identify two distinct regimes differing in modulation frequency and modulation strength. Longitudinal surface waves are generated either resonantly or parametrically for modulation frequencies near the radial trap frequency or twice the trap frequency, respectively. The dispersion of these waves, the latter being a Faraday wave, is well-reproduced by a mean-field theory that accounts for the 3D nature of the elongated condensate. In contrast, in the regime of lower modulation frequencies we find that no clear resonances occur, but with increased modulation strength, the condensate forms an irregular granulated distribution that is outside the scope of a mean-field approach. We find that the granulated condensate is characterized by large quantum fluctuations and correlations, which are well-described with single-shot simulations obtained from wavefunctions computed by a beyond mean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method.

Nonlinearities induced by parametric resonance in effectively 1D atomic Bose condensates

We present a numerical study of the dynamical effects following a sudden change of the transverse trapping frequency in an elongated Bose-Einstein condensate, which induces periodic oscillations of the radial density. At early times, we observe an exponential growth of the number of resonant longitudinal phonons, in agreement with the predictions of the Bogoliubov-de Gennes treatment. We then observe an ordered sequence of phenomena induced by the nonlinearities of the system. The first is a loss of the nonseparability of the resonant phonon pairs. This is followed by the saturation of the exponential growth and a strong depletion of condensed atoms. Notably, these effects are well-described by effective 1D dynamics, and are hardly affected by the damping of the radial oscillations. Finally, the atomic spectrum becomes broad, featureless and almost incoherent, in agreement with experimental results. The link between this sequence of events and the preheating scenario in inflationary cosmology is striking, as is the similarity of techniques used to study them.

Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate

New phenomena of collective light scattering are observed when an elongated Bose-Einstein condensate is pumped by two non-interfering beams counterpropagating along its long axis. In the limit of small Rayleigh scattering rates, the presence of a second pump beam suppresses superradiance, whereas at large Rayleigh scattering rates it lowers the effective threshold power for collective light scattering. In the latter regime, the quench dynamics of the two-beam system are oscillatory, compared to monotonic in the single-beam case. In addition, the dependence on power, detuning, and atom number is explored. The observed features of the two-beam system qualitatively agree with the recent prediction of a supersolid crystalline phase of light and matter at large Rayleigh scattering rates [S. Ostermann, F. Piazza, and H. Ritsch, Phys. Rev. X 6, 021026 (2016).]

Induced density correlations in a sonic black hole condensate

Analog black/white hole pairs, consisting of a region of supersonic flow, have been achieved in a recent experiment by J. Steinhauer using an elongated Bose-Einstein condensate. A growing standing density wave, and a checkerboard feature in the density-density correlation function, were observed in the supersonic region. We model the density-density correlation function, taking into account both quantum fluctuations and the shot-to-shot variation of atom number normally present in ultracold-atom experiments. We find that quantum fluctuations alone produce some, but not all, of the features of the correlation function, whereas atom-number fluctuation alone can produce all the observed features, and agreement is best when both are included. In both cases, the density-density correlation is not intrinsic to the fluctuations, but rather is induced by modulation of the standing wave caused by the fluctuations.

Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate.

We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.

Solitonic vortices in Bose–Einstein condensates

We analyse, theoretically and experimentally, the nature of solitonic vortices (SV) in an elongated Bose-Einstein condensate. In the experiment, such defects are created via the Kibble-Zurek mechanism, when the temperature of a gas of sodium atoms is quenched across the BEC transition, and are imaged after a free expansion of the condensate. By using the Gross-Pitaevskii equation, we calculate the in-trap density and phase distributions characterizing a SV in the crossover from an elongate quasi-1D to a bulk 3D regime. The simulations show that the free expansion strongly amplifies the key features of a SV and produces a remarkable twist of the solitonic plane due to the quantized vorticity associated with the defect. Good agreement is found between simulations and experiments.

Gray-body factor and infrared divergences in 1D BEC acoustic black holes

It is shown that the gray-body factor for a one-dimensional elongated Bose-Einstein condensate (BEC) acoustic black hole with one horizon does not vanish in the low-frequency ($\omega\to 0$) limit. This implies that the analog Hawking radiation is dominated by the emission of an infinite number ($\frac{1}{\omega}$) of soft phonons in contrast with the case of a Schwarzschild black hole where the gray-body factor vanishes as $\omega\to 0$ and the spectrum is not dominated by low-energy particles. The infrared behaviors of certain correlation functions are also discussed.

Modulated amplitude waves with non-trivial phase in quasi-1D inhomogeneous Bose–Einstein condensates

Abstract We consider a 1D nonlinear Schrodinger equation (NLSE) which describes the mean field dynamics of an elongated Bose–Einstein condensate and prove the existence of modulated amplitude waves with non-trivial phase and minimal spatial period tending to infinite. The proof combines the theory of local continuation of non-degenerate periodic solutions with a property of the Ermakov–Pinney equation.

Inelastic collisions of solitary waves in anisotropic Bose–Einstein condensates: sling-shot events and expanding collision bubbles

We study experimentally and theoretically the dynamics of apparent dark soliton stripes in an elongated Bose–Einstein condensate. We show that for the trapping strengths corresponding to our experimental setup, the transverse confinement along one of the tight directions is not strong enough to arrest the formation of solitonic vortices or vortex rings. These solitonic vortices and vortex rings, when integrated along the transverse direction, appear as dark soliton stripes along the longitudinal direction thereby hiding their true character. The latter significantly modifies the interaction dynamics during collision events and can lead to apparent examples of inelasticity and what may appear experimentally even as a merger of two dark soliton stripes. We explain this feature by means of the interaction of two solitonic vortices leading to a sling shot event with one of the solitonic vortices being ejected at a relatively large speed. Furthermore we observe expanding collision bubbles which consist of repeated inelastic collisions of a dark soliton stripe pair with an increasing time interval between collisions.

RYDBERG EXCITATION OF A BOSE-EINSTEIN CONDENSATE

Rydberg excitation of an elongated Bose-Einstein condensate is performed. We show how the dipole-blockade mechanism restricts the number of Rydberg atoms it is possible to excite in such a cloud. Using the super-atom model we then look at the feasibility of observing coherent effects in even stricter geometries, one dimensional optical lattices

Suppression of Faraday waves in a Bose-Einstein condensate in the presence of an optical lattice

We study the formation of Faraday waves in an elongated Bose-Einstein condensate in presence of a one-dimensional optical lattice, where phonons are parametrically excited by modulating the radial confinement of the condensate. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. By increasing the potential depth, the local sound velocity decreases and when it equals the condensate local phase velocity, the condensate becomes dynamically unstable and the parametric excitation of Faraday waves is suppressed.

Dynamics of dark–bright solitons in cigar-shaped Bose–Einstein condensates

We explore the stability and dynamics of dark–bright (DB) solitons in two-component elongated Bose–Einstein condensates by developing effective one-dimensional vector equations and solving the three-dimensional Gross–Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the DB soliton on the atom number of its components is found; importantly, the wave may become dynamically unstable even in the 1D regime. As the atom number in the dark-soliton-supporting component is further increased, spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom. Moreover, the interactions of two DB solitons are investigated with an emphasis on the importance of their relative phases. Experimental results showcasing multiple DB soliton oscillations and a DB–DB collision in a Bose–Einstein condensate consisting of two hyperfine states of 87Rb confined in an elongated optical dipole trap are presented.

High-order momentum modes by resonant superradiant scattering

The spatial and time evolutions of superradiant scattering are studied theoretically for a weak pump beam with different frequency components traveling along the long axis of an elongated Bose-Einstein condensate. Resulting from the analysis for mode competition between the different resonant channels and the local depletion of the spatial distribution in the superradiant Rayleigh scattering, a new method of getting a large number of high-order forward modes by resonant frequency components of the pump beam is provided, which is beneficial to a lager momentum transfer in atom manipulation for the atom interferometry and atomic optics.

Effective one-dimensional dynamics of elongated Bose–Einstein condensates

By using a variational approach in combination with the adiabatic approximation we derive a new effective 1D equation of motion for the axial dynamics of elongated condensates. For condensates with vorticity ∣ q∣ = 0 or 1, this equation coincides with our previous proposal [A. Muñoz Mateo, V. Delgado, Phys. Rev. A 77 (2008) 013617]. We also rederive the nonpolynomial Schrödinger equation (NPSE) in terms of the adiabatic approximation. This provides a unified treatment for obtaining the different effective equations and allows appreciating clearly the differences and similarities between the various proposals. We also obtain an expression for the axial healing length of cigar-shaped condensates and show that, in the local density approximation and in units of the axial oscillator length, it coincides with the inverse of the condensate axial half-length. From this result it immediately follows the necessary condition for the validity of the local density approximation. Finally, we obtain analytical formulas that give the frequency of the axial breathing mode with accuracy better than 1%. These formulas can be relevant from an experimental point of view since they can be expressed in terms only of the axial half-length and remain valid in the crossover between the Thomas–Fermi and the quasi-1D mean-field regimes. We have corroborated the validity of our results by numerically solving the full 3D Gross–Pitaevskii equation.

Collisions of Dark Solitons in Elongated Bose-Einstein Condensates

We present experimental data showing the head-on collision of dark solitons generated in an elongated Bose-Einstein condensate. No discernable interaction can be recorded, in full agreement with the fundamental theoretical concepts of solitons as mutually transparent quasiparticles. Our soliton generation technique allows for the creation of solitons with different depths; hence, they can be distinguished and their trajectories be followed. Simulations of the 1D-Gross-Pitaevskii equation have been performed to compare the experiment with a mean-field description.

Superradiant Rayleigh scattering from a Bose–Einstein condensate with the incident laser along the long axis

We have realized the superradiant Rayleigh scattering in an elongated Bose–Einstein condensate, where the pump laser pulse travels along the long axis. In this incident configuration the spatial asymmetries and the backward scattering pattern are reported. The spatial and temporal evolution of the superradiant process is analyzed by our semiclassical model.

Density modulations in an elongated Bose-Einstein condensate released from a disordered potential

We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time of flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder and not from initial phase fluctuations (thermal or quantum).